In many acoustic systems, such as piano strings
(§9.4.1,§C.6), wave propagation is also
significantly dispersive. A wave-propagation medium is said to
be dispersive if the speed of wave propagation is not the same at all
frequencies. As a result, a propagating wave shape will ``disperse''
(change shape) as its various frequency components travel at different
speeds. Dispersive propagation in one direction can be simulated
using a delay line in series with a nonlinear phasefilter, as
indicated in Fig.2.5. If there is no damping, the filter
must be all-pass [449], i.e.,
for
all
.

Figure 2.5:
Dispersive traveling-wave simulator. In
principle, the digital filter provides an arbitrary
nonnegative delay corresponding to one sample of wave
propagation at each frequency.